1 Introduction
1.1 Types of time series
1.2 Objectives of time-series analysis
2 Descriptive techniques
2.1 Components of a time series
2.2 Plotting the series and stationarity
2.3 Transformations
2.4 Estimating and removing the trend
2.5 The sample autocorrelation function
2.6 Practice problems
3 Stochastic processes
3.1 Strict stationarity
3.2 Second-order stationarity
3.3 Properties of the autocorrelation function
4 Purely random process
4.1 Definition and properties
5 Random walk
5.1 Definition and properties
5.2 Practice problems
6 Moving average processes
6.1 Definition and moments
6.2 The first-order moving average
7 Invertibility
7.1 The identification problem
7.2 The backward shift operator
7.3 Practice problems
8 Autoregressive processes
8.1 The first-order process
8.2 The general order
8.3 The second-order process
8.4 Practice problems
9 Mixed ARMA models
9.1 Definition
9.2 The \(\psi \) and \(\pi \) weights
9.3 The autocorrelation function
10 Integrated ARIMA models
10.1 Definition
10.2 How much to difference
10.3 Practice problems
11 Partial autocorrelation and model identification
11.1 The partial autocorrelation function
11.2 Identifying a model
11.3 Practice problems
12 Estimation of models
12.1 Estimating the mean
12.2 Fitting an autoregressive model
12.3 Fitting a moving average process
12.4 Practice problems
13 Diagnostic checking and model selection
13.1 The Box–Jenkins approach
13.2 Residual analysis
13.3 Portmanteau tests
13.4 Model selection criteria
13.5 Practice problems
14 Forecasting
14.1 Forecasting methods
14.2 Exponential smoothing
14.3 Holt and Holt–Winters methods
14.4 Box–Jenkins forecasts
14.5 Practice problems
15 Seasonal ARIMA models
15.1 Seasonal differencing
15.2 The multiplicative seasonal model
15.3 Forecasting seasonal models
15.4 Practice problems
16 The frequency domain
16.1 The spectral density
16.2 The periodogram
16.3 Practice problems
17 State space models and the Kalman filter
17.1 The linear model
17.2 The Kalman filter
18 Nonlinear models: ARCH and volatility
18.1 The ARCH and GARCH models
18.2 Practice problems
19 Review problems
19.1 Problems on the whole course